Competing structures in two-dimensional trapped dipolar gases

We study a system of dipolar molecules confined in a two-dimensional trap and subject to an optical square lattice. The repulsive long-range dipolar interaction D/r³ favors an equilateral triangular arrangement of the molecules, which competes against the square symmetry of the underlying optical lattice with lattice constant b and amplitude V. We find the minimal-energy states at the commensurate density n=1/b² and establish the complete square-to-triangular transformation pathway of the lattice with decreasing V involving period-doubled, solitonic, and distorted-triangular configurations.